Given that the fitted regression is Y = 76.40 − 6.388X1 + 0.870X2,the standard error of b1 is 1.453,and n = 63,at α = .05,we can conclude that X1 is a significant predictor of Y.

Question

Quizplus · Accepted Answer

To determine if X1 is a significant predictor of Y, we need to conduct a hypothesis test on the regression coefficient b1. Using the given standard error of b1 and n, we can calculate the t-statistic as:

t = ( b1 - 0 ) / SE(b1)
  = ( -6.388 - 0 ) / 1.453
  = -4.396

Assuming a two-tailed test at α = .05, the critical t-value for 61 degrees of freedom (n-2) is ±2.002. Since |-4.396| > 2.002, we reject the null hypothesis that b1 = 0, and conclude that X1 is a significant predictor of Y. Therefore, the answer is A.

Given That the Fitted Regression Is Y = 76